Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26255 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
814 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,24)(21,22)(23,25)(26,27,31,35)(28,33,37,41)(29,38,36,32)(30,40,39,34);(14,15)(16,17)(19,22)(23,24)(26,28,30,36,31,37,39,29)(27,32,34,33,35,38,40,41);(15,17)(26,29,39,37,31,36,30,28)(27,33,40,32,35,41,34,38);(18,20,21,25)(19,23,22,24)(26,29,39,37,31,36,30,28)(27,33,40,32,35,41,34,38)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19243);